I.V. Lomonosov

Wide-range multi-phase equations of state for metals

Abstract The generalization of available experimental and theoretical information is given in the form of a multi-phase wide-range equation of state (EOS). The semiempirical EOS model accounts for solid, liquid, gas and plasma states as well as two-phase regions of melting and evaporation. Results obtained on construction, calculation of the phase diagrams and thermodynamic properties of 30 simple and refractory metals are discussed. Major attention is given to the region of the phase diagram occupied by the hot dense liquid.

Target heating in high-energy-density matter experiments at the proposed GSI FAIR facility: Non-linear bunch rotation in SIS100 and optimization of spot size and pulse length

The Gesellschaft fur Schwerionenforschung ~GSI! Darmstadt has been approved to build a new powerful facility named FAIR ~Facility for Antiprotons and Ion Research! which involves the construction of a new synchrotron ring SIS100. In this paper, we will report on the results of a parameter study that has been carried out to estimate the minimum pulse lengths and the maximum peak powers achievable, using bunch rotation RF gymnastic-including nonlinearities of the RF gap voltage in SIS100, using a longitudinal dynamics particle in cell ~PIC! code, ESME. These calculations have shown that a pulse length of the order of 20 ns may be possible when no prebunching is performed while the pulse length gradually increases with the prebunching voltage. Three different cases, including 0.4 GeV0 u, 1G eV 0u, and 2.7 GeV0u are considered for the particle energy. The worst case is for the kinetic energy of 0.4 GeV0u which leads to a pulse length of about 100 ns for a prebunching voltage of 100 kV ~RF amplitude!. The peak power was found to have a maximum, however, at 0.5‐1.5kV prebunching voltage, depending on the mean kinetic energy of the ions. It is expected that the SIS100 will deliver a beam with an intensity of 1‐2 3 10 12 ions. Availability of such a powerful beam will make it possible to study the properties of high-energy-density ~HED! matter in a parameter range that is very difficult to access by other means. These studies involve irradiation of high density targets by the ion beam for which optimization of the target heating is the key problem. The temperature to which a target can be heated depends on the power that is deposited in the material by the projectile ions. The optimization of the power, however, depends on the interplay of various parameters including beam intensity, beam spot area, and duration of the ion bunch. The purpose of this paper is to determine a set of the above parameters that would lead to an optimized target heating by the future SIS100 beam.

High energy density and beam induced stress related issues in solid graphite Super-FRS fast extraction targets

Survival of the production target in successive experiments (with a repetition rate of 1xa0Hz) over an extended period of time is one of the key problems encountered in designing the Super-FRS (Superconducting Fragment Separator) at the future Facility forAntiprotons and Ion Research (FAIR). Because of the difficulties involved in construction of a liquid jet metal target, it is highly desirable to employ a solid production target at the Super-FRS. However, with the high beam intensities that will be available at the FAIR, the production target may be destroyed in a single experiment due to high specific energy deposition by the beam in the target material. The level of specific energy deposition can be reduced to an acceptable value by increasing the beam focal spot area. However, the spot size is limited by requirements of achieving good isotope resolution and sufficient transmission of the secondary beam through the system. The resolving power of the fragment separator is inversely proportional to the X-dimension of the focal spot whereas the transmission depends on Y-dimension only. It has been previously shown [Tahir et al., 2005c] that an elliptic focal spot with appropriate dimensions, will fulfill the above two conditions simultaneously and will also have a large enough area to reduce the specific energy deposition to an acceptable level for certain beam intensities of interest. In this paper we present numerical simulations of thermodynamic and hydrodynamic behavior of a solid graphite target that is irradiated by 1xa0GeV/u uranium beam in the intensity range of 1010xa0–1011 ions per bunch with a bunch lengthxa0=xa050xa0ns. These simulations have been carried out using a three-dimensional computer code, PIC3D, that includes elastic-plastic effects. This theoretical work has shown that up to a beam intensity of 1011 ions/bunch, one can employ a solid target while for higher intensities the target will be destroyed due to thermal stresses induced by the beam. It has also been found that a circular focal spot leads to minimum thermal stresses as it generates minimum pressure gradients compared to an elliptic focal spot, for the same specific energy deposition. Moreover, the stress level increases with an increase in the ellipticity of the focal spot. It is therefore recommended that one should use a circular focal spot for lower intensities provided that the criteria for isotope resolution and transmission are fulfilled.

Simulations of a solid graphite target for high intensity fast extracted uranium beams for the Super-FRS

Extensive numerical simulations have been carried out to design a viable solid graphite wheel shaped production target for the super conducting fragment separator experiments (Super-FRS) at the future Facility for Antiprotons and Ion Research (FAIR) using an intense uranium beam. In this study, generation, propagation and decay of deviatoric stress waves induced by the beam in the target, have been investigated. Maximum beam intensities that the target can tolerate using different focal spot sizes that are determined by requirements of good isotope resolution and transmission of the secondary beam through the fragment separator, have been calculated. It has been reported elsewhere that the tensile strength of graphite significantly increases with temperature. To take advantage of this effect, calculations have also been done in which the target is preheated to a higher temperature, that in practice can be achieved, for example, by irradiating the target with a defocused ion beam before the experiments are performed. We report results of a few examples using an initial temperature of 2000xa0K. This study has shown that employing such a configuration, one may use a solid graphite production target even for the maximum intensity of the uranium beam (5xa0×xa010 11 ion per bunch) at the Super-FRS.

Prospects of high energy density physics research using the CERN super proton synchrotron (SPS)

The Super Proton Synchrotron (SPS) will serve as an injector to the Large Hadron Collider (LHC) at CERN as well as it is used to accelerate and extract proton beams for fixed target experiments. In either case, safety of operation is a very important issue that needs to be carefully addressed. This paper presents detailed numerical simulations of the thermodynamic and hydrodynamic response of solid targets made of copper and tungsten that experience impact of a full SPS beam comprized of 288 bunches of 450 GeV/c protons. These simulations have shown that the material will be seriously damaged if such an accident happens. An interesting outcome of this work is that the SPS can be used to carry out dedicated experiments to study High Energy Density (HED) states in matter.

Numerical modeling of heavy ion induced stress waves in solid targets

The target is cylinder with a length = 7 mm and radius = 5 mm. One face of the cylinder is irradiated with a uranium beam having a particle energy of 400 MeV/u. The beam pulse consists of two bunches, each having a full width at half maximum (FWHM) of 80 ns and the total pule duration is 500 ns. The beam focal spot size (FWHM of the Gaussian power distribution in transverse direction) is as sumed to be 0.5 mm. Two different values for beam intensity, N are used.

High energy density physics problems related to liquid jet lithium target for Super-FRS fast extraction scheme

The new international facility for antiproton and ion research (FAIR), at Darmstadt, Germany, will accelerate beams of all stable isotopes from protons up to uranium with unprecedented intensities (of the order of 10 12 ions per spill). Planned future experiments include production of exotic nuclei by fragmentation/fission of projectile ions of different species with energies up to 1.5 GeV/u at the proposed super conducting fragment separator, Super-FRS. In such experiments, the production target must survive multiple irradiations over an extended period of time, which in case of such beam intensities is highly questionable. Previous work showed that with full intensity of the uranium beam, a solid graphite target will be destroyed after being irradiated once, unless the beam focal spot is made very large that will result in extremely poor transmission and resolution of the secondary isotopes. An alternative to a solid target could be a windowless liquid jet target. We have carried out three-dimensional numerical simulations to study the problem of target heating and propagation of pressure in a liquid Li target. These first calculations have shown that a liquid lithium target may survive the full uranium beam intensity for a reasonable size focal spot.

Proposed High Energy Density Physics Research Using Intense Particle Beams at FAIR: The HEDgeHOB Collaboration

Physics of high energy density (HED) matter is an ever-expanding field of research with very wide applications to basic and applied physics and with great potential for revolutionary technological and industrial applications. Over the past decades, static as well as dynamic configurations have been widely used to research this interesting field of science. Recent technological advances in the development of high-quality well-focused strongly bunched intense particle beams have led to the idea of generating samples of HED matter using isochoric and uniform heating of solid targets by such intense beams. Theoretical work reported in this paper explores the possibility of carrying out novel experiments using the future Facility for Antiprotons and Ion Research at Darmstadt.

The creation of strongly coupled plasmas using an intense heavy ion beam: low-entropy compression of hydrogen and the problem of hydrogen metallization

Intense heavy ion beams deposit energy very efficiently over extended volumes of solid density targets, thereby creating large samples of strongly coupled plasmas. Intense beams of energetic heavy ions are therefore an ideal tool to research this interesting field. It is also possible to design experiments using special beam–target geometries to achieve low-entropy compression of samples of matter. This type of experiments is of particular interest for studying the problem of hydrogen metallization. In this paper we present a design study of such a proposed experiment that will be carried out at the future heavy ion synchrotron facility SIS100, at the Gesellschaft fur Schwerionenforschung, Darmstadt. This study has been done using a two-dimensional hydrodynamic computer code. The target consists of a solid hydrogen cylinder that is enclosed in a thick shell of lead whose one face is irradiated with an ion beam which has an annular (ring shaped) focal spot. The beam intensity and other parameters are considered to be the same as expected at the future SIS100 facility. The simulations show that due to multiple shock reflection between the cylinder axis and the lead–hydrogen boundary, one can achieve up to 20 times solid density in hydrogen while keeping the temperature as low as a few thousand K. The corresponding pressure is of the order of 10 Mbar. These values of the physical parameters lie within the range of theoretically predicted values for hydrogen metallization. We have also carried out a parameter study of this problem by varying the target and beam parameters over a wide range. It has been found that the results are very insensitive to such changes in the input parameters.

Simulations of full impact of the Large Hadron Collider beam with a solid graphite target

AbstractThe Large Hadron Collider (LHC) will operate with 7 TeV/c protons with a luminosity of 10 34 cm 22 s 21 . This requires twobeams, each with 2808 bunches. The nominal intensity per bunch is 1.15 10 11 protons and the total energystored in eachbeam is 362 MJ. In previous papers, the mechanisms causing equipment damage in case of a failure of the machineprotection system was discussed, assuming that the entire beam is deflected onto a copper target. Another failurescenario is the deflection of beam, or part of it, into carbon material. Carbon collimators and beam absorbers areinstalled in many locations around the LHC close to the beam, since carbon is the material that is most suitable toabsorb the beam energy without being damaged. In case of a failure, it is very likely that such absorbers are hit first,for example, when the beam is accidentally deflected. Some type of failures needs to be anticipated, such as accidentalfiring of injection and extraction kicker magnets leading to a wrong deflection of a few bunches. Protection of LHCequipment relies on the capture of wrongly deflected bunches with beam absorbers that are positioned close to thebeam. For maximum robustness, the absorbers jaws are made out of carbon materials. It has been demonstratedexperimentally and theoretically that carbon survives the impact of a few bunches expected for such failures. However,beam absorbers are not designed for major failures in the protection system, such as the beam dump kicker deflectingthe entire beam by a wrong angle. Since beam absorbers are closest to the beam, it is likely that they are hit first in anycase of accidental beam loss. In the present paper we present numerical simulations using carbon as target material inorder to estimate the damage caused to carbon absorbers in case of major beam impact.Keywords: Collimators and beam; Large Hadron Collider; Stoppers; Warm dense matter